RT，想不懂标记永久化里面的sum如何在区间乘法中维护（这是标记永久化的代码

#include<iostream>
#include<cstdio>
#include<cstring>
#define ll long long

using namespace std;

ll n,m;
ll sum[400010],add[400010],a[100010];

void build(ll k,ll l,ll r) {
	if(l == r) {
		sum[k] = a[l];
		return;
	}
	ll mid = (l+r)/2;
	build(k*2,l,mid);
	build(k*2+1,mid+1,r);
	sum[k] += sum[k*2] + sum[k*2+1];
}

void Add(ll k,ll l,ll r,ll x,ll y,ll num) {
	if(l > y || r < x) return;
	if(l >= x && r <= y) {
		add[k] += num;
		return;
	}
	sum[k] += (min(r,y) - max(l,x) + 1) * num;
	ll mid = (l+r)/2;
	Add(k*2,l,mid,x,y,num);
	Add(k*2+1,mid+1,r,x,y,num);
}

ll query(ll k,ll l,ll r,ll x,ll y) {
	if(l > y || r < x) return 0;
	if(l >= x && r <= y) return sum[k] + add[k] * (r-l+1);
	long long res = 0;
	res += add[k] * (min(r,y) - max(x,l) + 1);
	ll mid = (l+r)/2;
	res += query(k*2,l,mid,x,y);
	res += query(k*2+1,mid+1,r,x,y);
	return res;
}

int main() {
	cin >> n >> m;
	for(ll i = 1;i <= n;i++) {
		cin >> a[i];
	}
	build(1,1,n);
	
	for(ll i = 1;i <= m;i++) {
		ll judge,x,y,k;
		cin >> judge;
		if(judge == 1) {
			cin >> x >> y >> k;
			Add(1,1,n,x,y,k);
		}
		else {
			cin >> x >> y;
			cout << query(1,1,n,x,y) << endl;
		}
	}
	
	return 0;
}